I have four halogen LV downlighters in my kitchen, controlled by one
dimmer switch. All of them use dimmer transformers. I once had to
change the chocolate box on one of them that melted, but other than
that they have given three years of trouble free operation.

Recently they have been failing to turn on. This affects all of the
lights, not just one. I noticed that if I turned the dimmer down (made
the light more dim) they would then come on, and turning the dimmer
back up would turn them off again.

It's rather intermittent, sometimes they turn on fine at full power,
other times not.

I took a look in the switch unit but all the connections seem fine
there.

Any other ideas?